Least Common Multiple (LCM) of 199 and 88
The least common multiple (LCM) of 199 and 88 is 17512.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 199 and 88?
First, calculate the GCD of 199 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 88 = 2 remainder 23 |
| 2 | 88 ÷ 23 = 3 remainder 19 |
| 3 | 23 ÷ 19 = 1 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 200 | 4200 |
| 109 and 179 | 19511 |
| 118 and 65 | 7670 |
| 193 and 161 | 31073 |
| 188 and 65 | 12220 |